
Example: Swimming Pool
Imagine that you have (or had) a summer job at a swimming pool. In preparation for the summer sun worshipers, you are asked to fill up the pool. To schedule the opening day, your boss wants to know how long it will take. Without any formal engineering background, most people would inquire about the size of the pumps, say 100 gpm (gallons per minute) and the capacity of the pool, say 150,000 gallons. Given this information, a quick calculation indicates that the pool will fill in 1,500 minutes. But why does this work out and more importantly what can you show me that will support your answer?
This is the question we consistently ask engineering students as they progress through their education. What happens when there is no answer in the back of the book? Whats the basis for your belief that your analysis is correct? Whats the physical law(s) that governs the your answer?
Taking a more fundamental approach to this apparently simple problem, the experienced problem solver recognizes that the underlying physical law is the conservation of mass (not the conservation of volume as often applied by many students). As developed in most fluid mechanics classes, students would first identify a control volume, say the volume of the water inside the pool at any time t, and apply the conservation of mass equation:
_{}
where the lefthand side represents the rate of change of the mass inside the control volume and the righthand side represents the net mass flow rate of water into the control volume. Now by a suitable set of assumptions this equation can be simplified as follows:
· Water is incompressible, therefore density is uniform in space and constant with time, thus _{} and _{}
· There is only one mass flow rate into the system, _{} .
Thus the conservation mass equation can be simplified as follows:
_{}
Thus for this particular problem, the rate of change of the volume of the system equals the volumetric flow rate of water into the system. Integrating both sides of the equation and assuming that the pump flow rate is a constant gives the following result:
_{}
This kind of methodical solution to a problem is a goal of engineering science education.
Typically engineering science, sometimes referred to as applied science, has worked to build student understanding, integration and application of concepts from firstyear science courses through a set of engineering science courses. In the courses, usually dynamics, thermodynamics, fluid mechanics and circuits, students improve their students problem solving skills in these specific disciplines. This does in fact improve their ability to solve problems within these individual areas; however, it does very little to help students begin to see the larger picture that many of us first understood in graduate school. To this end we believe that a unified framework, henceforth referred to as the Conservation and Accounting Framework, provides several benefits:
 It provides a common framework for developing/stating/understanding the basic physical laws of natureconservation of mass, momentum, energy, and charge, and entropy accounting (the Second Law of Thermodynamics).
 It provides a common framework for approaching the development of mathematical models of engineering systems.
 It highlights the similarities between many physical processes.
 It underscores the differences between and the role of physical laws, constitutive relations, definitions, and physical constraints.
 It highlights the importance and impact of making assumptions in modeling systems.
 It negates the need for through and across variables commonly stressed in systems engineering.
 It helps students recognize the interconnectedness of the world and how systems interact.
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References

Grinter, L.E. (Chair), Report on Evaluation of Engineering Education, American Society for Engineering Education, Washington, DC, 1955.

Harris, Eugene M. DeLoatch, William R. Grogan, Irene C. Peden, and John R. Whinnery, "Journal of Engineering Education Round Table: Reflections on the Grinter Report," Journal of Engineering Education, Vol. 83, No. 1, pp. 6994 (1994) (includes as an Appendix the Grinter Report, issued in September, 1955).

Glover, Charles, J., and Carl A. Erdman, "Overview of the Texas A&M/NSF Engineering Core Curriculum Development," Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 1114 November 1992, pp. 363367

Glover, Charles J., K. M. Lunsford, and John A. Fleming, TAMU/NSF Engineering Core Curriculum Course 1: Conservation Principles in Engineering, Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 1114 November 1992, pp. 603608

Glover, Charles J., K. M. Lunsford, and John A. Fleming, Conservation Principles and the Structure of Engineering, 3^{rd} edition, New York: McGrawHill College Custom Series, 1992

Pollock, Thomas C., TAMU/NSF Engineering Core Curriculum Course 2: Properties of Matter, Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 1114 November 1992, pp. 609613

Pollock, Thomas C., Properties of Matter, 3rd edition, New York: McGrawHill College Custom Series, 1992

Everett, Louis J., TAMU/NSF Engineering Core Curriculum Course 3: Understanding Engineering via Conservation, Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 1114 November 1992, pp. 614619

Everett, Louis J., Understanding Engineering Systems via Conservation, 2nd edition, New York: McGrawHill College Custom Series, 1992

Glover, Charles J. and H. L. Jones, TAMU/NSF Engineering Core Curriculum Course 4: Conservation Principles for Continuous Media, Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 1114 November 1992 Conference, pp. 620624

Glover, C. J. and H. L. Jones, Conservation Principles for Continuous Media, 2nd edition, New York: McGrawHill College Custom Series, 1992

Erdman, Carl A., Charles J. Glover, and V. L. Willson, Curriculum Change: Acceptance and Dissemination, Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 1114 November 1992, pp. 368372

B. A. Black, From Conservation to Kirchoff: Getting Started in Circuits with Conservation and Accounting, Proceedings of the 1996 Frontiers in Education Conference, Salt Lake City, Utah, 69 November 1996

Griffin, Richard B., Louis J. Everett, P. Keating, Dimitris C. Lagoudas, E. Tebeaux, D. Parker, William Bassichis, and David Barrow, "Planning the Texas A&M University College of Engineering Sophomore Year Integrated Curriculum," Fourth World Conference on Engineering Education, St. Paul, Minnesota, October 1995, vol. 1, pp. 228232.

Everett, Louis J., "Experiences in the Integrated Sophomore Year of the Foundation Coalition at Texas A&M," Proceedings, 1996 ASEE National Conference, Washington, DC, June 1996

Richards, Donald E., Gloria J. Rogers, "A New Sophomore Engineering Curriculum  The First Year Experience," Proceedings, 1996 Frontiers in Education Conference, Salt Lake City, Utah, 69 November 1996

Heenan, William and Robert McLaughlan, "Development of an Integrated Sophomore Year Curriculum, Proceedings of the 1996 Frontiers in Education Conference, Salt Lake City, Utah, 69 November 1996

Mashburn, Brent, Barry Monk, Robert Smith, TanYu Lee, and Jon Bredeson, "Experiences with a New Engineering Sophomore Year, Proceedings of the 1996 Frontiers in Education Conference, Salt Lake City, Utah, 69 November 1996

Everett, Louis J., "Dynamics as a Process, Helping Undergraduates Understand Design and Analysis of Dynamics Systems," Proceedings, 1997 ASEE National Conference,

Doering, E., Electronics Lab Bench in a Laptop: Using Electronics Workbench to Enhance Learning in an Introductory Circuits Course, Proceedings of the 1997 Frontiers in Education Conference, November 1997

Cornwell, P., and J. Fine, Mechanics in the RoseHulman Foundation Coalition Sophomore Curriculum, Proceedings of the Workshop on Reform of Undergraduate Mechanics Education, Penn State, 1618 August 1998

Cornwell, P., and J. Fine, Mechanics in the RoseHulman Foundation Coalition Sophomore Curriculum, to appear in the International Journal of Engineering Education

Cornwell, P. and J. Fine, Integrating Dynamics throughout the Sophomore Year, Proceeedings, 1999 ASEE Annual Conference, Charlotte, North Carolina, 2023 June 1999

Burkhardt, H. "System physics: A uniform approach to the branches of classical physics." Am. J. Phys. 55 (4), April 1987, pp. 344350.

Fuchs, Hans U. Dynamics of Heat. SpringerVerlag, New York, 1996.
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